New Covenant, Davidic Covenant, and Levitical Covenant: Jeremiah 33:14-22

¹⁴ ‘Behold, days are coming,’ declares the Lord, ‘when I will fulfill the good word which I have spoken concerning the house of Israel and the house of Judah. 15 In those days and at that time I will cause a righteous Branch of David to spring forth; and He shall execute justice and righteousness on the earth. ¹⁶ In those days Judah will be saved and Jerusalem will dwell in safety; and this is the name by which she will be called: the Lord is our righteousness.’ ¹⁷ For thus says the Lord, ‘David shall never lack a man to sit on the throne of the house of Israel; ¹⁸ and the Levitical priests shall never lack a man before Me to offer burnt offerings, to burn grain offerings and to prepare sacrifices continually.’”

¹⁹ The word of the Lord came to Jeremiah, saying, ²⁰ “Thus says the Lord, ‘If you can break My covenant for the day and My covenant for the night, so that day and night will not be at their appointed time, ²¹ then My covenant may also be broken with David My servant so that he will not have a son to reign on his throne, and with the Levitical priests, My ministers. ²² As the host of heaven cannot be counted and the sand of the sea cannot be measured, so I will multiply the descendants of David My servant and the Levites who minister to Me.’" (Jeremiah 33:14-22 NASB)

Notice that the above text links together the Davidic Covenant, the New Covenant, and the Levitical Covenant. (The "good word" in verse 14 refers to the New Covenant promise from Jeremiah 31:27ff.)

The book of Hebrews also brings these three themes together and proclaims that they find specific fulfillment in Christ. Hebrews discusses the Davidic Covenant, for example, in Hebrews 1:5. Hebrews mentions Jesus as our High Priest in chapters 3-5, then gives a rather extended consideration of both the Levitical priesthood and the New Covenant in chapters 7-10.